From hilbert space to common sense: A synthesis of recent progress in the interpretation of quantum mechanics

Abstract

A new interpretation of quantum mechanics can be proposed, relying upon several important results that have been made during the last decade or so. It relies upon 1. (i) Griffiths histories describing in detail the properties of a quantum system and submitted to consistency conditions allowing a clearcut distinction between meaningful and meaningless properties. 2. (ii) Semi-classical physics as it now appears in the light of modern mathematics (microlocal analysis) to provide a clearer relation between the classical macroscopic behavior and its quantum foundations. 3. (iii) The decoherence effect leading to the irreversible spontaneous diagonalization of the reduced density matrix for collective macroscopic variables and resulting in effective superselection rules eliminating linear superpositions of macroscopic states. 4. (iv) The fact that not all macroscopic systems behave classically. 5. (v) A new logical approach to the interpretation of quantum mechanics allowing to found common sense classical logic for macroscopic facts upon a unique well-defined quantum rule. These various advances can now be put together to provide a new, so-called logical interpretation of quantum mechanics where the whole description of the physical world, including ordinary facts and common sense intuition, are based upon precise quantum rules. Although this interpretation differs significantly from the Copenhagen interpretation in its basic assumptions, the practical consequences of both theories essentially coincide, except for a significant improvement concerning some previously paradoxical or objectionable features of the conventional interpretation.